Vectorial Kato inequality for $p$-harmonic maps with optimal constant

Andreas Gastel; Katarzyna Mazowiecka; Michał Miśkiewicz

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arXiv · 2503.05038

Vectorial Kato inequality for $p$-harmonic maps with optimal constant

Andreas Gastel·Katarzyna Mazowiecka·Michał Miśkiewicz

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Abstract

We derive the sharp vectorial Kato inequality for $p$-harmonic mappings. Surprisingly, the optimal constant differs from the one obtained for scalar valued $p$-harmonic functions by Chang, Chen, and Wei. As an application we demonstrate how this inequality can be used in the study of regularity of $p$-harmonic maps. Furthermore, in the case of $p$-harmonic maps from $B^3$ to $\mathbb{S}^3$, we enhance the known range of $p$ values for which regularity is achieved. Specifically, we establish that for $p \in [2, 2.642]$, minimizing $p$-harmonic maps must be regular.

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Andreas Gastel, Katarzyna Mazowiecka, Michał Miśkiewicz. 2025-03-06. Vectorial Kato inequality for $p$-harmonic maps with optimal constant. https://arxiv.org/abs/2503.05038

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